I'm a .NET developer and I need to learn Lucene so we can run a very large scale search service that removes entries that the end user doesn't have access to. (ie a User can search for all documents with clearance level 3 or higher, but not clearance level 2 or 1)
Where do I start learning, which products should I consider? To be honest, I'm a little overwhelmed, but I'm determined to figure it all out... eventually.
If you want a book that covers all the basics of Lucene, consider "Lucene in Action". Even though the code samples are Java, you can easily port them to .NET. Of course, there also are tonnes of resources on the web, such as SO and the Lucene mailing lists which should help you along.
For project you describe, you should look at Solr since it abstracts out lots of the issues of scalability etc. and via Solrnet can easily integrate into your .NET app. To restrict access by a level, your index documents should contain a field called "Level" (say) and in the background of your user query, you append the "Level:Level-1" query, using a boolean query construct.
At this stage, my recommendation would be to stay away from Hadoop (Apache Map-reduce implementation) for your project and stick with Solr. If you are however keen to learn about it. It too has a very useful book, you guessed it "Hadoop In Action" (also from Manning Publications).
You seem to be confused about what exactly each project (Lucene/Solr/Hadoop/etc) does. So the first thing to do would be understanding the purpose of each project. Read the docs and blogs about them. If possible, buy and read books about them.
For example, MapReduce and Hadoop have nothing to do with your security requirements. Hadoop is a platform for distributed, scalable computing. But Solr is scalable on its own. You might want to use Hadoop to distribute a crawler though (e.g. Nutch).